If your Chief Medical Dwarf isn't doing diagnosis tasks, he's probably too busy. Diagnosis is an annoyingly low-priority job, so the CMD would rather do basically anything else, even carting stuff from place to place around the fortress. I would turn off ALL other labors the CMD has turned on (except for diagnosis) until he gets off his butt and does his job. Of course, he might take the opportunity to go "on break" for a couple weeks, then take a drink for a while, then eat his seasonal meal, but that happens sometimes.
Of course, since you mentioned your injured dwarf has been Resting for over a year, most likely he is permanently disabled. Most dwarves will heal anything healable within 4-6 months, so if he hasn't healed yet, he probably ain't gonna. I recommend a topical application of magma; I find this tends to cure anything that refuses to heal in some other manner.